The official Blender documentation provides a method to get the “Specular” value for the PBR-material reflections if the “IOR” value is known. To get the “Specular” value from the “IOR” value, we can use the following equation:
Creating separate elements of procedural textures in Blender is quite simply – find the desired formula, rebuilt it using mathematical nodes, and as a result, get the desired shape. However, textures created this way have one feature – no tiling. Tiling – a cyclic texture duplication, most time is considered harmful, and professional 3D artists try to avoid texture tiling. But sometimes tiling is necessary, for example, when creating patterns or ornaments.
The procedural texture element is always created in a single instance. This is because all the mathematics that forms the actual procedural image is based on the initial data – coordinates that start from 0, spread out to infinity and not repeat. However, the same mathematics helps us to solve this problem.
All procedural textures in Blender are based on math. Even such irregular structures as “Voronoi” and “Noise” are actually generated according to the mathematical formulas. An exact mathematical algorithm is sewed up into each base material node to obtain the desired image as a result.
We can not specify such algorithms in Blender in the usual mathematical format. However, among other nodes, Blender provides us the “Math” nodes – the wrap over simple mathematical operations. Using these nodes we can build complex mathematical algorithms yourself, generating interesting textures.